Request a call back

Join NOW to get access to exclusive study material for best results

ICSE Class 9 Answered

D,E and F are the mid-points of the sides BC,CA and AB respectively of triangle ABC.Prove that: (1)BDEF is a parallelogram. (2)area of triangle BDEF is half the area of triangle ABC.
Asked by 151434255575758 | 10 Feb, 2018, 04:11: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon space In space increment ABC comma space straight d comma straight E comma straight F space are space the space mid space points space of space BC comma space CA comma space and space AB space respectively.
To space prove colon space square BDEF space is space parallelogram
space space space space space space space space space space space space space space space space space space space space space ar left parenthesis square space BDEF right parenthesis equals 1 half ar open parentheses increment ABC close parentheses
Proof colon space In space increment ABC
space space space space space space space space space space space space space straight F space and space straight E space are space mid space points space of space AB space and space AC space respectively.
space space space space space space space space space space space space space FE parallel to BC space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis BPT right parenthesis
space space space space space space space space space space space space space similarly comma space EF parallel to BD space and space ED parallel to BF
space space space space space space space space space space space space space Hence comma space square BDEF space is space parallelogram
space space space space space space space space space space space space space Similarly space we space can space show space that space square AFDE space and space square FDCE space are space parallelograms.
space space space space space space space space space space space space DF space is space diagonal space of space parallelogram.
space space space space space space space space space space space space ar open parentheses increment FBD close parentheses equals ar open parentheses increment DEF close parentheses.............. left parenthesis 1 right parenthesis
space space space space space space space space space space space space space ar left parenthesis square space BDEF right parenthesis equals ar open parentheses increment FBD close parentheses plus ar open parentheses increment DEF close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 ar open parentheses increment DEF close parentheses..................... from space left parenthesis 1 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 cross times 1 fourth ar open parentheses increment ABC close parentheses equals 1 half ar open parentheses increment ABC close parentheses
space space space space space space space space space space

end style
Answered by Sneha shidid | 12 Feb, 2018, 09:38: AM
Get Latest Study Material for Academic year 24-25 Click here
×